Problem: Simplify the following expression: $ x = \dfrac{-1}{5} + \dfrac{-8k + 9}{k - 10} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 10}{k - 10}$ $ \dfrac{-1}{5} \times \dfrac{k - 10}{k - 10} = \dfrac{-k + 10}{5k - 50} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-8k + 9}{k - 10} \times \dfrac{5}{5} = \dfrac{-40k + 45}{5k - 50} $ Therefore $ x = \dfrac{-k + 10}{5k - 50} + \dfrac{-40k + 45}{5k - 50} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-k + 10 - 40k + 45}{5k - 50} $ $x = \dfrac{-41k + 55}{5k - 50}$